The use of dynamic software to potentially enhance conceptual understanding and a productive disposition in the visual learning of algebra: an interventionist case study
- Authors: Junius, Daniel Franscius
- Date: 2023-10-13
- Subjects: Mathematics education , Algebra Study and teaching (Secondary) Namibia , Educational technology , Visual learning , GeoGebra , High school students Attitudes
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/431542 , vital:72784 , DOI 10.21504/10962/431542
- Description: Over the decades, the didactics and practice of teaching mathematics has offered many unique challenges and opportunities for exploration and understanding. The introduction and development of technology into mathematics is one of the occurrences which has also contributed to a new discourse in teaching mathematics – in this case the teaching of algebra. Algebra is still seen as a gatekeeper and remains as one of the key reasons for a negative disposition amongst learners towards learning the subject. Across the globe psychologists, philosophers and educators continue to engage in debates and research projects in search of answers and solutions for the improvement of algebra teaching and an improvement in dispositions towards learning algebra. This thesis reports on a research project that focused on the use of dynamic software to enhance the conceptual understanding and productive dispositions of selected learners through the visual learning of abstract algebraic concepts. The research was executed as an interventionist case study. A case study methodological strategy was adopted with two groups of 30 Grade 9 learners. One group was a Grade 9 mathematics class of a school in Windhoek who scored above average in algebra but showed a very low disposition score, while the other group was made up of learners from a community project who scored high on the disposition scale but achieved below average results in algebra. The analytical framework of the case study is structured around a combination of complementary algebraic topics presented through visual learning, with GeoGebra as a medium of instruction. With the focus on visualisation and the use of technology the study investigated and attempted to understand how participants processed and internalised algebraic concepts to make sense of abstract algebraic concepts and eventually gain sustained conceptual understanding. The study was framed by the theoretical theories of constructivism and the Dual Coding Theory. For the collection of data, a mixed methods approach was adopted following three cycles. Three algebraic topics were taught with GeoGebra applets yielding both qualitative and quantitative data, through the observation of participants, screen captures and reflective interviews, using instruments designed specifically for the study and collecting quantitative achievement test results. The study, a journey that both the participants and the researcher embarked upon, revealed that the use of technology enhanced conceptual understanding for both groups and both groups showed a positive change in disposition towards learning algebra. The intervention with GeoGebra consistently and progressively improved in terms of conceptual understanding and dispositions towards learning algebra significant improvements in results were achieved. The findings showed that this approach to teaching algebra yielded positive results and gave new insights into visual teaching with technology. New opportunities for further research were created. , Thesis (PhD) -- Faculty of Education, Secondary and Post-School Education, 2023
- Full Text:
- Date Issued: 2023-10-13
- Authors: Junius, Daniel Franscius
- Date: 2023-10-13
- Subjects: Mathematics education , Algebra Study and teaching (Secondary) Namibia , Educational technology , Visual learning , GeoGebra , High school students Attitudes
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/431542 , vital:72784 , DOI 10.21504/10962/431542
- Description: Over the decades, the didactics and practice of teaching mathematics has offered many unique challenges and opportunities for exploration and understanding. The introduction and development of technology into mathematics is one of the occurrences which has also contributed to a new discourse in teaching mathematics – in this case the teaching of algebra. Algebra is still seen as a gatekeeper and remains as one of the key reasons for a negative disposition amongst learners towards learning the subject. Across the globe psychologists, philosophers and educators continue to engage in debates and research projects in search of answers and solutions for the improvement of algebra teaching and an improvement in dispositions towards learning algebra. This thesis reports on a research project that focused on the use of dynamic software to enhance the conceptual understanding and productive dispositions of selected learners through the visual learning of abstract algebraic concepts. The research was executed as an interventionist case study. A case study methodological strategy was adopted with two groups of 30 Grade 9 learners. One group was a Grade 9 mathematics class of a school in Windhoek who scored above average in algebra but showed a very low disposition score, while the other group was made up of learners from a community project who scored high on the disposition scale but achieved below average results in algebra. The analytical framework of the case study is structured around a combination of complementary algebraic topics presented through visual learning, with GeoGebra as a medium of instruction. With the focus on visualisation and the use of technology the study investigated and attempted to understand how participants processed and internalised algebraic concepts to make sense of abstract algebraic concepts and eventually gain sustained conceptual understanding. The study was framed by the theoretical theories of constructivism and the Dual Coding Theory. For the collection of data, a mixed methods approach was adopted following three cycles. Three algebraic topics were taught with GeoGebra applets yielding both qualitative and quantitative data, through the observation of participants, screen captures and reflective interviews, using instruments designed specifically for the study and collecting quantitative achievement test results. The study, a journey that both the participants and the researcher embarked upon, revealed that the use of technology enhanced conceptual understanding for both groups and both groups showed a positive change in disposition towards learning algebra. The intervention with GeoGebra consistently and progressively improved in terms of conceptual understanding and dispositions towards learning algebra significant improvements in results were achieved. The findings showed that this approach to teaching algebra yielded positive results and gave new insights into visual teaching with technology. New opportunities for further research were created. , Thesis (PhD) -- Faculty of Education, Secondary and Post-School Education, 2023
- Full Text:
- Date Issued: 2023-10-13
How do teachers characterise their teaching for conceptual understanding and procedural fluency?: a case study of two teachers
- Junius, Daniel Franscius, Danie Junius
- Authors: Junius, Daniel Franscius , Danie Junius
- Date: 2013
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia Mathematics -- Study and teaching -- Case studies
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: vital:1360 , http://hdl.handle.net/10962/d1001426
- Description: Over many years the practice or art of teaching Mathematics posed itself as, not only being different from the practice of teaching any other subject, but to have many challenges and opportunities that ask for exploration and understanding. Just after independence in 1990, Namibia has embarked upon a reform process for the entire education system. Many changes were brought about to create a uniform, equal system for all. However, many challenges still remain to be addressed. Mathematics education remains one of the key areas where Namibian teachers can contribute towards the improvement of the subject. Unsatisfactory results, under-qualified teachers, and a negative disposition towards Mathematics are some of the challenges. These challenges are not unique to Namibia. Across the globe psychologists, philosophers and educators continue to engage in debates and research projects in search of answers and solutions for the improvement of Mathematics education. Despite encountering numerous obstacles, many teachers are dedicated and achieve outstanding results with their learners. This thesis reports on a research project that focused on the Mathematics teaching practice of two teachers whose experiences can make a positive contribution to the improvement of Mathematics teaching in Namibia. Furthermore, this case study investigated and attempted to understand the Mathematics teaching practices of two proficient teachers who each claimed to have a specific and unique approach to teaching Mathematics. The one claimed to be mainly procedural in her Mathematics teaching, while the other one claimed to teach mainly in a conceptual manner. Both achieve very good results with their classes and attribute their own teaching orientations to a process of several experiences they went through as students and in their careers. The study revealed that both claims are substantiated and that each teacher was consistent in her claimed approach. Many challenges and constraints were encountered by both teachers, but in their unique and specific ways each teacher’s chosen teaching approach supported them to overcome these. It was evident from the findings that each teacher’s practice came about as an evolutionary process over an extended period of time. As many challenges and limitations are universal, it is believed that in sharing experiences, teachers can benefit from each other by improving their practice. It was clearly stated by both participants that the re-thinking of and reflecting on their own practices provided them with new insights and motivation. Peer support and sharing of practices contribute positively towards the improvement of the teachers’ classroom practices.
- Full Text:
- Date Issued: 2013
- Authors: Junius, Daniel Franscius , Danie Junius
- Date: 2013
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia Mathematics -- Study and teaching -- Case studies
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: vital:1360 , http://hdl.handle.net/10962/d1001426
- Description: Over many years the practice or art of teaching Mathematics posed itself as, not only being different from the practice of teaching any other subject, but to have many challenges and opportunities that ask for exploration and understanding. Just after independence in 1990, Namibia has embarked upon a reform process for the entire education system. Many changes were brought about to create a uniform, equal system for all. However, many challenges still remain to be addressed. Mathematics education remains one of the key areas where Namibian teachers can contribute towards the improvement of the subject. Unsatisfactory results, under-qualified teachers, and a negative disposition towards Mathematics are some of the challenges. These challenges are not unique to Namibia. Across the globe psychologists, philosophers and educators continue to engage in debates and research projects in search of answers and solutions for the improvement of Mathematics education. Despite encountering numerous obstacles, many teachers are dedicated and achieve outstanding results with their learners. This thesis reports on a research project that focused on the Mathematics teaching practice of two teachers whose experiences can make a positive contribution to the improvement of Mathematics teaching in Namibia. Furthermore, this case study investigated and attempted to understand the Mathematics teaching practices of two proficient teachers who each claimed to have a specific and unique approach to teaching Mathematics. The one claimed to be mainly procedural in her Mathematics teaching, while the other one claimed to teach mainly in a conceptual manner. Both achieve very good results with their classes and attribute their own teaching orientations to a process of several experiences they went through as students and in their careers. The study revealed that both claims are substantiated and that each teacher was consistent in her claimed approach. Many challenges and constraints were encountered by both teachers, but in their unique and specific ways each teacher’s chosen teaching approach supported them to overcome these. It was evident from the findings that each teacher’s practice came about as an evolutionary process over an extended period of time. As many challenges and limitations are universal, it is believed that in sharing experiences, teachers can benefit from each other by improving their practice. It was clearly stated by both participants that the re-thinking of and reflecting on their own practices provided them with new insights and motivation. Peer support and sharing of practices contribute positively towards the improvement of the teachers’ classroom practices.
- Full Text:
- Date Issued: 2013
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